**4.4. Systematic uncertainties in the determination of
_{m}**

The above values differ sensitively from several recent analyses on the
same
test and using the same high redshift sample. It is therefore important to
identify the possible source of systematic uncertainty that may explain
these differences. The test is based on the evolution of the mass function
(Blanchard and Bartlett, 1998).
The mass function has to be related to the
primordial fluctuations. The Press and Schechter formalism is generally
used for this, and this is what used in deriving the above numbers.
However, this may be slightly
uncertain. Using the more recent form proposed by
Governato et al. (1999)
we found a value for
_{m}
slightly higher (a different mass function was used in
Figure 1). A second problem lies
in the mass temperature
relation which is necessary to go from the mass function to the temperature
distribution function. The mass can be estimated either from the
hydrostatic equation or from numerical simulations. In general
hydrostatic equation leads to mass smaller than those found in numerical
simulations
(Roussel et al., 2000;
Markevitch, 1998;
Reiprich and
Böhringer, 2002;
Seljak, 2002).
Using the
two most extreme mass-temperature relations inferred from numerical
simulations, we found a 10% difference. We concluded that such
uncertainties are not critical.

Another serious issue is the local sample used: using HA sample
we found a value smaller by 40%. Identically, if we postulated that the
high redshift abundance has been underestimated by a factor of two,
_{m}
is reduced by 40%. The determination of the selection function of EMSS
is therefore critical. An evolution in the morphology of clusters with
redshift would result in a dramatic change in the inferred abundance
(Adami et al., 2001).
This is the most serious possible uncertainty in this
analysis. However, the growing evidences for the scaling of observed
properties of distant clusters
(Neumann and Arnaud,
2001),
rather disfavor such possibility.